The path of a cannon ball is modeled by the quadratic
f(x) = - 16x
2 + 120x + 10.
The graph in red and black show the same function.
What similarities and differences to do you see?

Answer:

[tex]22^\circ + m\angle C = 90^\circ[/tex]

Step-by-step explanation:

Pre-Solving:

We are given that [tex]\angle A[/tex] (which is equal to 22°) and [tex]\angle B[/tex] are vertical angles, and that [tex]\angle B[/tex] is complementary to [tex]\angle C[/tex].

We want to write an equation that will help us solve [tex]\angle C[/tex].

Solving:

Recall that vertical angles are congruent by vertical angles theorem.

This means that [tex]\angle A \cong \angle B[/tex]; it also means that the measure of [tex]\angle B[/tex] is also 22°.

Also recall that complementary angles add up to 90°.

This means that [tex]m\angle B + m\angle C = 90^\circ[/tex].

Since we deduced that [tex]m\angle B[/tex] is 22°, we can substitute that value into the equation.

Hence, an equation that can be used to solve for [tex]\angle C[/tex] is:

[tex]22^\circ + m\angle C = 90^\circ[/tex]

Answer:

m∠A = m∠B

m∠A = 22°

m∠B + m∠C = 90°

Step-by-step explanation:

∠A and ∠B are vertical angles. (Given)

By definition of vertical angles, a pair of angles with the same vertex and that are on opposite sides of two intersecting straight lines are congruent.

It is given that ∠A is 22°, and is a vertical angle with ∠B.

∴ ∠A ≅ ∠B (Definition of Vertical Angles).

IF m∠A = 22° and ∠A ≅ ∠B, THEN m∠B = 22° (Transitive Property of Equality).

∠B is complementary with ∠C (Given)

m∠B + m∠C = 90° (given).

m∠B = 22° (⇒Transitive Property of Equality)

Plug in 22 for m∠B in the given equation:

22 + m∠C = 90

Isolate the term, m∠C. Note the equal sign, what you do to one side, you do to the other. Subtract 22 from both sides of the equation:

m∠C + 22 (-22) = 90 (-22)

m∠C = 90 - 22

m∠C = 68°

~

Therefore, your system of equation will be:

m∠A = m∠B

m∠A = 22°

m∠B + m∠C = 90°

~

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Answer: 55

Step-by-step explanation:

I believe you are talking about a triangle.

This is soo easy, you got this you professional.

Find x:

10 + 4x-5+ + 2x - 5 = 180

Add like terms

6x = 180

x=30

Find BC:

2(30) - 5

55

BC = 55

The given information can be summarized as follows:

Team: Cleveland Cavaliers

Height (in inches): 73, 75, 77, 79, 81

Range: 81 - 73 = 8

IQR: Q3 - Q1 = 81 - 75 = 6

Median: 79

Team: LA Clippers

Height (in inches): 76, 80, 83, 85

Range: 85 - 76 = 9

IQR: Q3 - Q1 = 85 - 80 = 5

Median: 81.5 (average of 80 and 83)

Using this information, we can evaluate the given statements:

#1: The LA Clippers have a greater variability of heights than the Cleveland Cavaliers.

This statement is true. The range of the LA Clippers' heights (9) is greater than the range of the Cleveland Cavaliers' heights (8).

#2: The shortest team member is 76 inches.

This statement is true. The LA Clippers have a player with a height of 76 inches, which is shorter than any player on the Cleveland Cavaliers.

#3: The second quartile of the LA Clippers is equal to the second quartile of the Cleveland Cavaliers.

This statement is false. The second quartile (or median) of the LA Clippers (81.5) is higher than the second quartile (or median) of the Cleveland Cavaliers (79).

#4: The median of the LA Clippers is approximately 80 inches.

This statement is true. The median of the LA Clippers is 81.5, which rounds to approximately 80 inches.

a. The independent variable in this function is the amount of time a car is parked, measured in hours. The dependent variable is the cost of parking, measured in dollars.

b. "The cost of parking is a function of the amount of time a car is parked."

c. Here is a possible graph of the function:

           ^

           |

   $12     +--------/-----

           |      /      

           |    /        

           |  /          

   $3      o              

           |              

           |              

           |              

           +--------------->

                 Time

In this graph, the vertical axis represents the cost of parking in dollars, and the horizontal axis represents the amount of time a car is parked in hours. The graph shows a linear relationship between the two variables, with a slope of $3 per hour, up to a maximum cost of $12. This means that the cost of parking increases by $3 for each additional hour of parking, up to a maximum cost of $12.

The theoretical probability is 0.5 and the experimental probability is 0.583

Part A:

Since the coin is fair, the probability of it landing on heads is 0.5 or 50%.

The theoretical probability of a fair coin landing on heads is 0.5.

Part B:

Let's denote the outcome of flipping the coin as H (heads) or T (tails). We flip the coin 12 times and record the frequency of each outcome:

NB: This is an assumption and not a given data;

Outcome Frequency

    H              7

    T                      5

The experimental probability of landing on heads is calculated by dividing the number of times the coin landed on heads by the total number of coin flips:

Experimental probability of landing on heads = number of heads / total number of flips

Experimental probability of landing on heads = 7 / 12 = 0.583

Part C:

Comparing the experimental probability to the theoretical probability, we can see that they are different. The theoretical probability is 0.5, while the experimental probability is 0.583. This difference can be attributed to the randomness of the coin flips and the fact that we only flipped the coin 12 times, which is a relatively small sample size. As we increase the number of coin flips, the experimental probability should converge to the theoretical probability.

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a. To rationalize the expression √√√4 + x = 3 3, we need to get rid of the cube roots in the denominator.

First, we simplify the cube root of 4:

√√√4 = √√2

So, our expression becomes:

√√2 + x = 3 3

To get rid of the cube root in the denominator, we need to multiply both sides by the conjugate of the denominator:

(3 - √2)(√√2 + x) = 3

Expanding the left side:

3√√2 + 3x - 2√2 - √2√√2x = 3

Simplifying:

3x - 2√2 - √2√√2x = 3 - 3√√2

Combining like terms:

(3 - √2)x = 3 - 3√√2 + 2√2

Simplifying:

(3 - √2)x = (3 + 2√2) - 3√√2

Dividing both sides by (3 - √2):

x = [(3 + 2√2) - 3√√2]/(3 - √2)

Simplifying:

x = (3 + 2√2)(3 + √2)/7

b. To rationalize and solve for x in the expression 1-√2:

We need to get rid of the radical in the denominator by multiplying both the numerator and denominator by its conjugate:

1 - √2 / 1 - √2 * 1 + √2 / 1 + √2

Simplifying, we get:

(1 - √2)(1 + √2) / (1 - √2)(1 + √2)

= 1 - 2

= -1

So, x = -1.

Therefore, the rationalized expressions are:

a. √√2 + x = (3 + 2√2)(3 + √2)/7

b. 1-√2 = -1

Answer:

  7 cm

Step-by-step explanation:

You want the edge length of a cube whose space diagonal is 7√3 cm.

The square of the face diagonal of a cube of edge length s is ...

  d² = s² +s² = 2s²

The square of the space diagonal is found by applying the Pythagorean theorem again. The space diagonal is the hypotenuse of a right triangle whose legs are one cube edge and the face diagonal.

  D² = s² +d² = s² +2s² = 3s²

  D = √(3s²) = s√3

So, we want to find s when D = 7√3:

  s√3 = 7√3

  s = 7

The edge length of the cube is 7 cm.

The length οf the bar that shοuld be inserted tο make the ring fit the finger is apprοximately 12.57 millimeters.

Length οf bar = π × (new diameter - οriginal diameter), where π is the cοnstant pi, and new diameter and οriginal diameter are in millimeters.

The οriginal diameter οf the ring is 20 millimeters, and the new diameter that the ring needs tο fit is 16 millimeters.

Therefοre, the length οf the bar that shοuld be inserted is:

length οf bar = π × (16 - 20)

= π × (-4)

≈ -12.57 millimeters

Since the length οf the bar cannοt be negative, we can assume that it shοuld be 12.57 millimetres lοng.

Therefοre, the length οf the bar that shοuld be inserted tο make the ring fit the finger is apprοximately 12.57 millimeters.

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The smallest number of eggs that could have been in the basket = 301

Given that the basket is filled with an unknown number of eggs.

Let N be the smallest number of eggs in the basket.

When eggs are removed 2, 3, 4, 5, or 6 at a time, one egg is left over at the end which means (N-1) is divisible by 2, 3, 4, 5, or 6, i.e. (N-1) is the least common multiple of 2, 3, 4, 5, and 6.  

Since LCM (2, 3, 4, 5, 6) = 60

So, (N-1) should be a multiple of 60, then only (N-1) will be divisible by 2, 3, 4, 5, and 6. Therefore N is of the form 60k+1 (where k is an integer).

Since no egg is left over when they are removed 7 at a time, N should be a multiple of 7. Smallest multiple of 7 that is of the form 60k+1 (where k is an integer) is 301.

Hence the smallest number of eggs that could have been in the basket = 301.

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So, the area of the composite figure is 96.57 square centimeters.

In geometry, area refers to the measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters, square feet, or square centimeters.

To find the area of a shape, you need to measure the length and width of the shape and then multiply those measurements together. The formula for calculating the area of a rectangle, for example, is length x width. The formula for calculating the area of a circle is pi x radius squared, where pi is a mathematical constant, and the radius is the distance from the center of the circle to its edge.

by the question.

sure, I can help you with that!

To find the area of the composite figure, we need to find the area of each individual shape and then add them up.

First, let's find the area of the sector of the circle. We know that the radius of the circle is 6 cm, and the central angle of the sector is 82% of a full circle. Since a full circle has 360 degrees, we can find the central angle of the sector by multiplying 360 by 0.82:

[tex]Central angle of sector = 360 x 0.82 = 295.2 degrees[/tex]

The area of the sector can be found using the formula:

Area of sector = (central angle/360) x π x radius^2

Substituting the values, we know:

[tex]Area of sector = (295.2/360) x 3.14 x 6^2 = 56.57 cm^2[/tex]

Next, let's find the area of the triangle. We know that the base of the triangle is 8 cm, and the height is 10 cm. We can use the formula for the area of a triangle:

[tex]Area of triangle = 1/2 x base x height[/tex]

Substituting the values, we know:

[tex]Area of triangle = 1/2 x 8 x 10 = 40 cm^2[/tex]

Now, we can add the areas of the sector and the triangle to find the total area of the composite figure:

Total area = area of sector + area of triangle

[tex]Total area = 56.57 + 40 = 96.57 cm^2[/tex]

Rounding this to the nearest hundredth, we get:

[tex]Total area =96.57 cm^2[/tex]

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the answer to the question is 5.20XY cubed.

How to solve the problem?

The square root of 18 X to the seventh power Y to the sixth power can be simplified using the laws of exponents and radicals. First, we can express 18 as a product of its prime factors: 18 = 2 x 3 x 3. Then, we can write X to the seventh power as X to the sixth power times X, and Y to the sixth power as Y to the third power squared.

So, we have:

Square root of 18 X to the seventh power Y to the sixth power

= Square root of (2 x 3 x 3) X to the sixth power X Y to the third power squared

= Square root of 2 X to the sixth power Y to the third power squared times 3

= Square root of 2 X to the sixth power Y to the third power squared times square root of 3

Using the laws of exponents and radicals, we can simplify the square root of 2 X to the sixth power Y to the third power squared as X cubed Y cubed, and we can approximate the square root of 3 as 1.73. Therefore:

Square root of 18 X to the seventh power Y to the sixth power

= X cubed Y cubed times square root of 3

= 3XY cubed times 1.73

= 5.20XY cubed (rounded to two decimal places)

So, the answer to the question is 5.20XY cubed.

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Answer:

6, 2, and 3 would all also be 64° angles. 1, 4, 5, and 8 would all be 116° angles.

Step-by-step explanation:

Since 64° and 5 make up a supplementary angle (180°) just do the equation 180°-64° to get 116°. From there know that 64° and angle 6 must be equal (using the same logic from supplementary angles) then angles 2 and 3 must also be equal. Then apply that to angle 5 (which is 116°) and angle 8, as well as angles 1 and 4.

The standard error of the average sample weight is 7.32 when 15 participants are randomly selected for the sample, rounded to two decimal places

The standard error of the average sample weight is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard error of the average sample weight is 35/√15 = 7.32. Thus, the standard error of the average sample weight is 7.32 when 15 participants are randomly selected for the sample. To calculate the standard error of the average sample weight, it is important to first determine the standard deviation of the population.

The standard deviation of the population, in this case, is 35. This is because it was found from the historical data that the weight of the participants is normally distributed with a mean of 175 lbs and a standard deviation of 35 lbs. Next, the standard deviation is divided by the square root of the sample size. In this case, the sample size is 15 participants. Thus, the standard deviation is divided by the square root of 15 (√15) which results in the standard error of the average sample weight which is 35/√15 = 7.32.

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The standard error of the average sample weight when 15 participants are randomly selected for the sample is       9.03 lbs. .

The standard error measures the accuracy with which a sample distribution represents a population by using standard deviation.

The formula for calculating the standard error of the mean is as follows:

Standard error = σ/√n

Where, σ = Standard deviation and n = sample size

Given that the standard deviation is 35 pounds, and the sample size is 15.

Therefore,

Standard error = σ/√n= 35/√15

= 35/3.873

= 9.0369 lbs

Rounded 9.0369 lbs to two decimal places we get, 9.03 lbs

Hence, the standard error of the average sample weight is 9.03 lbs when 15 participants are randomly selected for the sample.

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The odds of answering at least 9 questions correctly out of 15 by choosing at random is approximately 0.120

To solve this problem, we can use the binomial distribution, which models the probability of getting a certain number of successes in a fixed number of independent trials, each with the same probability of success.

In this case, we have 15 independent trials (the 15 questions) and the probability of success in each trial is 1/4 (the probability of guessing the correct answer among 4 choices). We want to find the probability of getting at least 9 successes.

Using a binomial distribution calculator, we can calculate this probability as

P(X ≥ 9) = 1 - P(X < 9) = 1 - binomcdf(15, 1/4, 8) ≈ 0.120

where binomcdf is the cumulative distribution function of the binomial distribution, which gives the probability of getting up to a certain number of successes (in this case, up to 8). The complement of this probability (1 minus the probability of getting up to 8 successes) gives the probability of getting at least 9 successes.

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The correct response is (D) since insufficient data exist to establish the number of junction points.

A circle is a geometric shape made up of all points in a plane that are equally spaced apart from a specific point known as the circle's center. The diameter of a circle is the distance through its center; the radius of the circle is the distance from any point on the circle to that point. A circle's circumference, which is measured around it, is equal to either two times the radius or one time the diameter. Several branches of mathematics, science, and engineering make use of circles.

given

Knowing the equation of the circle is necessary to figure out how many spots the line with the equation y = -3/4x + 25/4 touches the circle.

We are unable to calculate the number of points of intersection without this information.

The correct response is (D) since insufficient data exist to establish the number of junction points.

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the area of the first sector piece is approximately 42.4115 square . and area of the second sector piece is approximately 149.03 cm².centimeters.

what is area of circle?

The area of a circle is given by the formula,where A is the area of the circle, r is the radius of the circle, and π (pi) is a mathematical constant that is approximately equal to 3.14159.In words, the area of a circle is equal to pi times the square of its radius.

In the given question,

The area of a sector of a circle is given by the formula:

A = (θ/360) * πr²

where:

θ is the angle at the center of the circle (in degrees)

r is the radius of the circle

π is the mathematical constant pi (approximately equal to 3.14)

In this case, the angle at the vertex of the sector piece is 60 degrees, and the radius is 9 cm. Therefore, the area of the sector piece is:

A = (60/360) * π * 9²

A = (1/6) * π * 81

A = 13.5π

A ≈ 42.4115 cm²

So the area of the sector piece is approximately 42.4115 square centimeters

A = π(8.4 cm)²

A = 221.76 cm²

Next, we need to find the fraction of the circle that corresponds to the given angle. The total angle of a circle is 360 degrees, so the fraction of the circle that corresponds to an angle θ in degrees is:

f = θ/360

Plugging in the given angle of 242 degrees, we have:

f = 242/360

f = 0.6722

So the area of the sector piece is:

A_sector = f * A

A_sector = 0.6722 * 221.76 cm²

A_sector = 149.03 cm²

Therefore, the area of the sector piece is approximately 149.03 cm².

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The area of the sector of for the given radius is 1. 42.4 cm² and 2. 152.9 cm².

A sector of a circle is an area that is bounded by two circle radii and the arc that runs between them. The length of the arc is proportional to the circumference of the circle, and the angle formed by the radii is known as the sector's central angle. The formula  A = (θ/360)πr² may be used to determine the area of a sector, where r denotes the radius of the circle, denotes the constant pi, and denotes the central angle in degrees.

The area of a sector can be calculated using the formula:

A = (θ/360)πr²

1. For r = 9 and theta = 60 we have:

A = (60/360)π(9)² ≈ 42.4 cm²

2. For r = 8.4 and theta = 242 we have:

A = (242/360)π(8.4)² ≈ 152.9 cm²

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The part 7 is closed and the part 8 is not closed where as the part 6 is neither open nor closed.

What is close polynomial and open polynomial?

The terms "closed polynomial" and "open polynomial" are not commonly used in mathematics. However, we can talk about sets of polynomials being open or closed.

In general, a set of polynomials is said to be open if, for any polynomial in the set, there is a small "neighborhood" of polynomials around it that is also contained in the set. Intuitively, this means that the set "opens up" in all directions around any point in the set.

A set of polynomials is said to be closed if it contains all of its limit points. In other words, if a sequence of polynomials in the set converges to a polynomial outside of the set, then that polynomial must be added to the set to make it closed.

For example, the set of all quadratic polynomials with a nonzero discriminant is closed under addition, scalar multiplication, and multiplication of polynomials, so it is a closed set. The set of all cubic polynomials with real coefficients is an open set, since for any cubic polynomial, we can find a small "neighborhood" of cubic polynomials around it by adjusting the coefficients slightly.

6.The polynomial set {(x² + x − 4) - (x²+x+8)} is equivalent to the set {-12}. A single point set like this is neither open nor closed in the usual topologies on the real numbers.

7.The polynomial set (2-x)(1 + 3x) is the set of all polynomials of degree at most 2 with a leading coefficient of -3. This set is closed under addition, scalar multiplication, and multiplication of polynomials, so it is a closed set.

8.The polynomial set (5b-3c)(7b - 3c) is equivalent to the set {25b² - 36bc + 9c²}, which is the set of all quadratic polynomials in b and c with a nonzero discriminant. This set is not closed under addition, since the sum of two polynomials in this set can have a zero discriminant. Therefore, it is not a closed set.

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Answer:

Step-by-step explanation:

3/5 x 100= 60%

Step-by-step explanation:

5 % decrease means 95 %  (.95)  remain

Year 1

   800 * .95

   year 2  800 * .95  * .95

       .

       .

        year 5 = 800(.95)^5 = 619 deer after year 5

Answer: To write 6^-5 in expanded form, we need to first recall the definition of negative exponents. If a number a is raised to a negative exponent, it means that we take the reciprocal of a raised to the absolute value of the exponent. In other words:

a^(-n) = 1 / a^n

Using this definition, we can write:

6^-5 = 1 / 6^5

Now, we can expand 6^5 using repeated multiplication or by using a calculator. 6^5 means 6 multiplied by itself five times:

6^5 = 6 × 6 × 6 × 6 × 6 = 7776

Therefore, we can write:

6^-5 = 1 / 6^5 = 1 / 7776

So, the expanded form of 6^-5 is 1/7776.

Step-by-step explanation:

Answer:

can you like write it out normally please, i can answer it then

Step-by-step explanation:

Step-by-step explanation:

The area of the rectangle can be calculated by multiplying its length and width. In this case, the length is 17 units and the width is 4 units.

Area = Length x Width

Area = 17 x 4

Area = 68 square units

Therefore, the area of the rectangle is 68 square units.

Answer:

1/2 + 1/8 + 1/3 + 1/2 + 1/8 + 1/3 = 23/12 = 1 (11/12)

Answer:  A. x= 12 and -2

Step-by-step explanation:

x-5= 7  Solve for positive answer

x= 7+5=12

x-5= -7 Solve for negative answer

x= -7+5=-2

Answer:

£2947

Step-by-step explanation:

the formula for simple interest is interest = prt.

p is the principal value, or what omar had at the beginning.

r is the rate at that you gain interest.

t is the amount of time in years.

so, plugging in our values, we multiply 2800*3*0.0175 to get 147.

now, since that was the amount of interest omar gained, we still have to add the original amount that he had, and 2800+147 = 2947.

so, the answer is £2947.

The 280 square foot lawn is in the designated area of a rectangular park that the city mayor wishes to use for gardening.

An object's area is how much space it takes up in two-dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The square-unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The rectangular park's allocated area is intended to be used by the city's public school for gardening courses.

The remaining area of the park will be developed into a lawn.

What is the lawn's formula?

The lawn's area is equal to the sum of its triangular and rectangle areas.

Lawn Area = 14 × 16 +.5 × 8 × 14

A = 224 + 56

A = 280 Ft²

Therefore, the correct option is 280ft² which is option C.

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Answer:

x=m+10

Step-by-step explanation:

Ur just making it into an equation

:)

In a game of chance, the probability of winning 50 is 40 percent and the probability of having to pay 50 is 60 percent. Therefore, the expected value of this game is -10. The correct answer is option A.

To find out what the expected value of this game is, we will need to use the formula:

Expected value (E) = (probability of winning x amount won) - (probability of losing x amount lost)

Let's substitute the values given in the question:

Probability of winning = 0.4

Amount won = 50

Probability of losing = 0.6

Amount lost = 50

Expected value (E) = (0.4 x 50) - (0.6 x 50)

                               = 20 - 30

                               = -10

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The probability that your mail will be delivered before 2 pm for 2 consecutive days is 0.81.

Given,

The probability that your mail is delivered before 2 pm is 0.90.

To find:The probability that your mail will be delivered before 2 pm for 2 consecutive days

Probability that your mail will be delivered before 2 pm for 1 day = 0.90

Probability that your mail will be delivered before 2 pm for 2 consecutive days = P(1st day before 2pm) and

P(2nd day before 2pm)P(1st day before 2pm) and P(2nd day before 2pm) = 0.90 × 0.90= 0.81

Hence, The probability that your mail will be delivered before 2 pm for 2 consecutive days is 0.81.

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